Velocity factor

Short description: Measure of electromagnetic transmission

The velocity factor (VF)[1] of a transmission medium is the ratio of the speed at which a wavefront (of an electromagnetic signal, a radio signal, a light pulse in an optical fibre or a change of the electrical voltage on a copper wire) passes through the medium, to the speed of light in vacuum. For optical signals, the velocity factor is the reciprocal of the refractive index.

The speed of radio waves in vacuum, for example, is the speed of light, and so the velocity factor of a radio wave in vacuum is 1.0 (unity). In air, the velocity factor is ~0.9997. In electrical cables, the velocity factor mainly depends on the insulating material (see table below).

In the computer networking and cable industries, the terms velocity of propagation (VoP or vP) and wave propagation speed is also used to mean a ratio of speeds.[2] In a general science and engineering context, these terms would be understood to mean an actual speed or velocity, with dimension of distance per time (and units such as metres per second),[3] while velocity factor is used for the ratio.

## Contents

* 1 Typical velocity factors
* 2 Calculating velocity factor
* 2.1 Electric wave
* 2.2 Optical wave
* 3 See also
* 4 References

## Typical velocity factors

Velocity factor is an important characteristic of communication media such as category 5 cables and radio transmission lines. Plenum data cable typically has a VF between 0.42 and 0.72 (42% to 72% of the speed of light in vacuum) and riser cable around 0.70 (approximately 210,000,000 m/s or 4.76 ns per metre).

Minimum velocity factors allowed for network cable standards  VF
(%) | Cable type | Ethernet physical layer

|
|

74~79%

| Cat-7 twisted pair |

77%

| RG-8/U | Minimum for 10BASE5[4]

67%

| Optical fiber (silica glass) | Minimum for 10BASE-FL,[5]
100BASE-FX, ...

67%

| Plastic optical fiber (PMMA) | 1000BASE-RHx

63%

| Plastic optical fiber (polystyrene)

65%

| RG-58A/U | Minimum for 10BASE2[6]

65%

| Cat-6A twisted pair | 10GBASE-T

64%

| Cat-5e twisted pair | 100BASE-TX, 1000BASE-T

58.5%

| Cat-3 twisted pair | Minimum for 10BASE-T[7]

Some typical velocity factors for radio communications cables provided in handbooks and texts are given in the following table:[8][9]

(%) | Transmission line | Center insulation

|
|

95~99%

| open-wire line ("ladder line") | air insulated

93%

| HJ8-50B 3 inch Heliax coaxial cable | air dielectric[10]

86%

| RG-8 Belden 7810A coaxial cable | gas-injected foamed
high-density polyethylene[11]

83%

| RG-6 Belden 1189A coaxial cable,
RG-11 Belden 1523A coaxial cable |

82%

| RG-8X Belden 9258 coaxial cable | foamed polyethylene dielectric

80%

| Belden 9085 twin-lead |

77%

| RG-8/U generic | foamed polyethylene

66%

| Belden 8723 twin shielded
stranded twisted pair | polypropylene insulator[12]

66%

| RG-213 CXP213 | solid polyethylene dielectric

## Calculating velocity factor

### Electric wave

VF equals the reciprocal of the square root of the dielectric constant (relative permittivity), κ or ϵr, of the material through which the signal passes:

VF=1κ

in the usual case where the relative permeability, μr, is 1. In the most general case:

VF=1μrϵr

which includes unusual magnetic conducting materials, such as ferrite.

The velocity factor for a lossless transmission line is given by:

VF=1c0L′C′

where L′ is the lineic inductance (inductance per length, in henries per metre), C′ is the lineic capacitance (capacitance per unit length) between the two conductors (capacitance per length, in farads per metre), and c0 is the speed of light in vacuum.

### Optical wave

VF equals the reciprocal of the refractive index n of the medium, usually optical fiber.

VF=1n

## See also

* Coaxial cable
* Propagation delay
* Signal velocity
* Speed of electricity
* Speed of sound
* Telegrapher's equations

## References

1. ↑ Gottlieb, I.M., Practical RF power design techniques, TAB Books, 1993, ISBN 0-8306-4129-7, p.251 ('velocity factor')
2. ↑ Velocity of Propagation, General Cable Australia Pty Ltd, retrieved 2010-02-13
3. ↑ "velocity of propagation" in Walker, P.M.B., Chambers Science and Technology Dictionary, Edinburgh, 1991, ISBN 1-85296-150-3
4. ↑ IEEE 802.3 Clause 8.4.1.3 The minimum required velocity of propagation is 0.77 c.
5. ↑ IEEE 802.3 clause 15.3.1.3 The propagation delay shall be ≤5 μs/km. (This is equivalent to a velocity of propagation of 0.67c.)
6. ↑ IEEE 802.3 Clause 10.5.1.3 The minimum required velocity of propagation is 0.65 c.
7. ↑ IEEE 802.3 Clause 14.4.2.4 The maximum propagation delay of twisted pair shall be 5.7 ns/m (minimum velocity of 0.585 × c).
8. ↑ Silver, H. Ward, ed (2011). "Chapter 22: Component Data and References". The ARRL Handbook for Radio Communications (88th ed.). Newington, CT: ARRL. p. 22.48. ISBN 978-0-87259-096-0.
9. ↑ Kaiser, Kenneth L. (2005). Transmission Lines, Matching, and Crosstalk. Boca Raton, FL: CRC Press. pp. 2–24. ISBN 978-0-8493-6362-7. https://books.google.com/books?id=QWFd-33xXvgC&pg=SA2-PA24.
10. ↑ "HJ8-50B". https://www.commscope.com/globalassets/digizuite/112335-p360-hj8-50b-external.pdf?r=1.
11. ↑ ﻿Belden Global Catalog﻿ (Report). 7810A. https://catalog.belden.com/techdata/EN/7810A_techdata.pdf.
12. ↑ "8723 multi-conductor, shielded twisted pair cable". http://www.belden.com/techdatas/english/8723.pdf.

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